A circular global profit Malmquist productivity index in data envelopment analysis

To remove the difficulty caused by different profit frontiers in different periods of time for calculating profit efficiency changes and its components, this paper proposes a circular global profit Malmquist productivity index. This index is applicable when the input costs and output prices are known and when producers seek to maximize the total profit of their decision making units (DMUs). To this end, first, two methods are introduced to obtain the common costs and prices with or without the decision maker's preferences, and then, a common profit efficient frontier is obtained. The proposed index can be decomposed into several circular components, viz., profit efficiency change, profit technical change, technical efficiency change, allocative efficiency change, technical change, and cost/price change. The proposed index is then generalised to compare the productivity of two different units at two different points in time. The global profit Malmquist productivity index developed here is unique and is computed using nonparametric linear programming model known as data envelopment analysis (DEA), and there is no need to resort to the geometric mean in the calculation. To illustrate the proposed index and its components, numerical examples at three successive periods of time are given.